Method and apparatus for determining stiffness of a roadway

ABSTRACT

An apparatus for the compaction of roadway materials includes a compaction analyzer for calculating stiffness during construction of the roadway. The apparatus generates a dynamic modulus for each layer of a roadway which can be used to calculate the overall effective modulus. A method for determining stiffness includes generating a dynamic modulus for each layer and calculating the overall effective modulus using the modulus of each layer.

CROSS REFERENCE TO RELATED APPLICATIONS

Priority is claimed from U.S. Provisional Application Ser. No. 61/621,259, entitled “Method of Determining Stiffness” filed Apr. 6, 2012.

BACKGROUND OF THE INVENTION

The current disclosure is directed to methods and apparatus for the compaction of roadway materials, and more particularly, to methods and apparatus for calibrating a compaction analyzer, and determining stiffness during construction.

Asphalt is often used as pavement. In the asphalt paving process, various grades of aggregate are used. The aggregate is mixed with asphalt cement (tar) and sand, and heated to approximately 150° C. to 169° C., and a paver lays down the hot asphalt mix and levels the asphalt mix with a series of augers and scrapers. The material as laid is not dense enough due to air voids in the asphalt mix. Therefore, a roller makes a number of passes over the layer of asphalt material, referred to herein as the asphalt mat, driving back and forth, or otherwise creating sufficient compaction to form asphalt of the strength needed for the road surface, or an individual pavement layer.

One of the key process parameters that is monitored during the compaction process is the compacted density of the asphalt mat. While there are many specifications and procedures to ensure that the desired density is achieved, most of these specifications require only 3-5 density readings per lane mile. Typically, the density readings will be from extracted roadway cores. The process of measuring density of the asphalt mat during the compaction process is cumbersome, time-consuming, and is not indicative of the overall compaction achieved unless measurements are taken at a large number of points distributed in a grid fashion, which is difficult to achieve in the field due to cost considerations alone. Failure to meet the target density is unacceptable and remedial measures may result in significant cost overruns. Because the density cannot be measured directly, researchers have attempted different methods for indirect measurements. Some of these are identified and described in U.S. Pat. No. 8,190,338 entitled Method and Apparatus for Compaction of Roadway Materials.

Stiffness is likewise a key design factor that directly impacts the load bearing capacity of roadway pavements. Early deterioration of pavements due to rutting, fatigue cracking, and other types of distresses may be attributed to inadequate stiffness achieved during the compaction process. The stiffness of a pavement is typically expressed in terms of modulus. While the dependence of pavement performance on stiffness is well known, stiffness is rarely measured or monitored in the field during pavement construction. Remedial measures to rectify inadequate compaction after pavement has cooled down are costly and time consuming. Since pavement is designed to have adequate strength and stiffness to withstand traffic load, it is desirable to know the stiffness of finished pavement layers. While density of an asphalt mix is a measure of its quality it does not directly provide information of the performance of the pavement under loading conditions. Stiffness on the other hand directly impacts the performance of a pavement under traffic loads. There is thus a need for apparatus and methods that provide for measurement and monitoring of stiffness during the compaction process.

SUMMARY OF THE INVENTION

The apparatus disclosed herein comprises a vibratory compactor, or roller, with sensors, and a compaction analyzer associated therewith. The compaction analyzer has a feature extraction module, a neural network module and an analyzer module. The sensors may comprise accelerometers for measuring vibratory response signals of the roller, and the compaction analyzer utilizes the characteristics of the vibratory response signals to generate, in real time, a modulus signal representative of the density of the material being compacted. In addition, the compaction analyzer will generate signals representative of the dynamic modulus of the pavement. A method of compacting a roadway section with a roller having a compaction analyzer operably associated therewith comprises entering initial input parameters into the compaction analyzer and making a plurality of passes with the roller over a layer of a portion of the roadway section. The method may further comprise applying a vibratory energy to the portion of the roadway section with the roller as it moves over the layer of the portion of the roadway section and repeatedly gathering responsive vibration signals of the roller as it moves over the layer portion of the roadway section. Additional steps may comprise generating, with the compaction analyzer, estimated modulus signals representative of estimated dynamic moduli based upon the responsive vibration signals of the roller and the initial input parameters entered into the compaction analyzer and measuring the modulus of the layer of the roadway section at a plurality of locations on the portion of the roadway section. The measured moduli may be compared to the estimated moduli at the plurality of locations to determine the difference between the measured and the estimated moduli. Selected ones of the initial input parameters to the analyzer can then be adjusted based on the difference between the measured moduli and the estimated moduli. The compaction analyzer will generate an adjusted modulus output signal which will more closely approximate an actual modulus of the roadway section than does the estimated modulus signal. The remainder of the layer of the roadway section is rolled until the compaction analyzer with the adjusted input parameters generates a desired adjusted output modulus signal. The method is performed on each layer of a multi-layer roadway section and an effective modulus for the multi-layer roadway section is determined using the modulus for each layer.

Another method may comprise entering initial input parameters into the compaction analyzer and making a plurality of passes over a layer of a portion of the roadway section. Vibratory energy may be applied to a portion of layer the roadway section as the plurality of passes are made, responsive vibratory signals of the roller generated in response to the applied vibratory energy are gathered. Selected responsive vibratory signals may be designated as corresponding to specified compaction levels, and the compaction levels of the portion of the roadway section representative of the responsive vibratory signals delivered in real time to an analyzer module in the compaction analyzer as the roller moves along the portion of the roadway section. An estimated modulus is generated in real time with the compaction analyzer based on the delivered compaction level and the initial input parameters as the roller rolls along the portion of the roadway. Modulus measurements of the portion of the roadway section may be taken at a plurality of locations on each layer of the portion of the roadway section to determine a measured modulus at each of the plurality of locations on each layer. The estimated modulus generated by the compaction analyzer at the plurality of locations is compared with the measured modulus at the plurality of locations, and selected ones of the initial input parameters are adjusted based upon the differences between the estimated modulus and the measured modulus. An adjusted modulus of the layer roadway section is generated in real time based upon the delivered compaction levels and the adjusted input parameters that more closely approximate the actual modulus than did the estimated modulus. An effective modulus for the multi layer roadway section is determined based on the modulus of each layer.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of a roller with a compaction analyzer.

FIG. 2 is a schematic representation of the compaction analyzer components.

FIG. 3 is exemplary and shows spectral features at an instant in time.

FIG. 4 is a spectrogram, and shows a five-second data set for passes made by the roller.

FIG. 5 shows the power content of the signals represented in FIG. 4.

FIG. 6 is a section showing multiple layers of the roadway.

DESCRIPTION OF A PREFERRED EMBODIMENT

The current disclosure is directed to methods and apparatus for compacting a roadway, and for using, and calibrating an Intelligent Asphalt Compaction Analyzer (IACA). The current disclosure is likewise directed to a method of determining the dynamic modulus of a roadway, which is a measure of the stiffness of the roadway.

FIG. 1 schematically shows the IACA 5, a device that can measure the density of an asphalt pavement continuously in real time, over the entire length of the pavement during its construction. Quality control techniques currently used in the field involve the measurement of density at several locations on the completed pavement or the extraction of roadway cores. These methods are usually time-consuming and do not reveal the overall quality of the construction. Furthermore, any compaction issues that are identified cannot be easily remedied after the asphalt mat has cooled down.

In recent years, several Intelligent Compaction (IC) technologies have been introduced by manufacturers of vibratory compactors. Uniform compaction of both soil and aggregate bases is achieved through the variation of the machine parameters (amplitude and frequency of vibrations, vectoring of the thrust, etc.). Dynamic control of the machine parameters allows for the application of the vibratory energy only to under-compacted areas and thereby preventing over-compaction and ensuring uniform compaction of the soil/aggregate base. While these IC techniques hold promise for the future, their performance is yet to be fully evaluated. Further, these IC products require the purchase of a new vibratory compactor that is equipped with the technology.

In contrast to the IC technologies being offered in the market place today, IACA 5 is a measurement device that does not control any aspect of the machine behavior. Further, IACA 5 is a stand-alone device that can be retrofitted on any existing vibratory compactor. A primary utility of IACA 5 is in providing real-time measurements of the density of the asphalt mat at each location on the pavement under construction. This information can be utilized by the roller operator to ensure uniform compaction, address under-compaction, as well as prevent over-compaction of the pavement.

IACA 5, as shown in FIG. 1, functions on the hypothesis that the vibratory roller, for example vibratory roller 10, and the underlying pavement material, which may be, for example, Hot Mix Asphalt (HMA) form a coupled system. The response of vibratory roller 10 is determined by the frequency of its vibratory motors and the natural vibratory modes of the coupled system. Compaction of an asphalt mat increases its stiffness and as a consequence, the vibrations of the compactor are altered. The knowledge of the properties of the pavement material and the vibration spectrum of the compactor can therefore be used to estimate the stiffness of the asphalt mat. Quality specifications for HMA are generally specified as a percentage of air voids so that, for example, 100% density means no air voids exist, and 90% density means 10% air voids exist. Since the quality specifications are usually specified as percentage air void content or as a percentage of the Maximum Theoretical Density (MTD) of the asphalt mat, IACA 5 can estimate the compacted density of the pavement.

Referring now to the drawings, vibratory compactor, or roller 10 is shown in FIG. 1. Vibratory compactor 10 which may be, for example, a DD-138 HFA Ingersoll Rand vibratory compactor, includes forward and rear drums 12 and 14, Forward drum 12 has an eccentric weight 16 mounted therein, and if desired, both forward and rear drums 12 and 14 may have eccentric weights 16 mounted therein. Eccentric weights 16 are rotated by motors (not shown), so that the rotation of the weights 16 within drums 12 and 14 cause an impact at the contact between drums 12 and 14 and a base 18, which may be comprised of HMA. Base 18 may be referred to as asphalt mat 18. The spacing between impacts is a function of the speed of the roller 10, and the speed of the eccentric weights 16, and may be, for example, 10-12 impulses per linear foot. Sensor module 22 associated with IACA 5 consists of accelerometers 24 mounted to frame 30 for measuring the vibrations of the compactor 10 during operation and may include infrared temperature sensors 26 for measuring the surface temperature of the asphalt base. Accelerometer 24 and temperature sensors 26 may be mounted to a frame 30 of roller 10. Sensors 26 essentially comprise a real-time data acquisition system. IACA 5 may include a user interface 28 which may be an Intel Pentium based laptop for specifying the amplitude and frequency of the vibration motors, and to input mat properties such as the mix type and lift thickness. User interface 28 will also be utilized to enter other initial input parameters as will be explained in more detail hereinbelow. Accelerometer 24 may be a CXL10HF3 tri-axial accelerometer manufactured by Crossbow, capable of measuring 10 g acceleration up to a frequency of 10 kHz. The surface temperature of asphalt mat 18 may be measured using an infrared temperature sensor 26 mounted on the frame 30. A global positioning system (GPS) 32 may also be mounted to roller 10. The GPS will, as is known in the art provide locations of roller 10 and will be coordinated with IACA 5 so that the location of the densities generated by IACA 5 will be known. GPS receiver 32 may be, for example, a Trimble Pro XT GPS receiver used to record the location of the roller 10 as it moves.

IACA 5 includes a feature extraction (FE) module 34 which computes the Fast Fourier Transform (FFT) of the input signal and extracts features corresponding to vibrations at different salient frequencies. The input signals are the responsive vibratory signals of roller 10, which results from the impacts made by the eccentric weights 16. The responsive vibratory signals are measured, or gathered by accelerometer 24. IACA 5 also includes a Neural Network (NN) Classifier 36 which is a multi-layer Neural Network that is trained to classify the extracted features into different classes, where each class represents a vibration pattern specific to a pre-specified level of compaction. Compaction analyzer module 38 in IACA 5 post-processes the output of the neural network and estimates the degree of compaction in real time. Each component of IACA 5 will be described in more detail hereinbelow.

Feature extractor module 34 implements a Fast Fourier Transform to efficiently extract the different frequency components of the responsive vibratory signals of roller 10. The output of the FFT is a vector with 256 elements, where each element corresponds to the normalized signal power at the corresponding frequency. The normalized signal power, as is understood, is the square of the amplitude at the frequency, so the extracted features are frequencies, and amplitudes at the frequencies. FIG. 3 is an example of the spectral features of vibratory signals, and shows frequencies, and the normalized power (i.e., squares of amplitudes) of the frequencies. The vibration signal of the roller 10 is sampled at a rate of 1 kHz (1000 Hz/sec), Because the responsive vibration signal of the roller 10 is sampled at 1 kHz, it is understood that the frequency spectrum is uniformly distributed from 0 to 500 Hz. Since the FFT output is a sector with 256 elements, the features are extracted in frequency bands of approximately 2 Hz. Features may be extracted eight times per second in an overlapping fashion, such that the input to the neural network 36 will include 128 elements from the previous instant at which features were extracted, and 128 elements from the current or immediate feature extraction.

Neural network classifier 36 is a three layer neural network with 200 inputs, 10 nodes in the input layer, 4 nodes in the hidden layer, and 1 node in the output layer. The inputs of the neural network correspond to the outputs of the feature extraction module, i.e., in this case 200 features in the frequency spectrum. In the preferred embodiment, only the upper 200 features in the frequency spectrum (i.e., from 100-500 Hz) are considered. Those in the lower range represent the frequency of roller 10 and may be ignored. Neural network 36 will classify the vibratory response signals of roller 10 into classes representing different levels of compaction.

The output of feature extraction module 34 is analyzed over several roller passes during the calibration process and the total power content in the responsive vibration signal of roller 10 is calculated at each instant in time. The power calculation is set forth hereinbelow. A minimum power level, a maximum power level, and equally spaced power levels are identified and the features of the vibratory response signal that correspond to the identified power levels are used to train the neural network 36. The identified minimum, maximum and equally spaced power levels are designated as corresponding to specified levels of compaction. During the compaction process, the neural network 36 observes the features of the responsive vibration signals of the roller and classifies the features as corresponding to one of the levels of compaction.

The plurality of pre-specified compaction levels will be identified, or designated with a number. In the case where five compaction levels are specified, a minimum compaction level can be identified, or designated as compaction level 0, and a maximum compaction level can be designated as compaction level 4. The compaction levels therebetween can be designated as compaction levels 1, 2 and 3 which correspond to the equally spaced power levels between the minimum and maximum power levels. FIG. 3 is exemplary, and shows features corresponding to five different compaction levels, with the lowest level corresponding to the case where the roller is operating with the vibration motors turned on and designated as level 0, level 4 designated as corresponding to the case where the maximum vibration is observed, and levels 1 through 3 corresponding to spaced levels therebetween.

The initial calibration of IACA 5 assumes that compaction level 0 corresponds to a lay-down density of the asphalt mat and the compaction level 4 corresponds to the target density as specified in the mix design sheet (designed at 100 gyrations of the superpave gyratory compactor). The lay-down density of asphalt is generally assumed to be, for example, 85% to 88%, and the target or maximum density will generally be 94-97%. Compaction levels 1, 2 and 3 are designated as corresponding to equally spaced densities therebetween.

During the calibration operation, roller 10 will make several passes on asphalt mat 18. Asphalt mat 18 may include a portion 40 of a roadway section 42 to be compacted. The portion 40 will comprise a defined length, for example, thirty feet. Locations will be identified on the portion of the roadway, marked as locations A, B, C, D and E on FIG. 11. The locations will be used to obtain actual measured densities of the portion 40 of the roadway section 42. It is understood that roadway section 42 may extend for several miles and that once the calibration described herein has occurred, rolling of the remainder of the roadway section 42 can occur without further actual measurement of the density so long as the roadway section is comprised of the same roadway material as portion 42, based upon the output of the IACA 5 as indicated on an IACA display 44.

As roller 10 makes a plurality of passes over the portion 40 of roadway section 42, eccentric weights 16 will generate impacts as described herein. Responsive vibratory signals of roller 10 are gathered by accelerometer 24 as roller 10 moves along portion 40 by accelerometer 24.

Roller 10 will cease making passes when the responsive vibratory signals become consistent, which indicates that no further change in compaction is occurring. Roller 10 should stop, for example, before rollover occurs.

The power content of the responsive vibratory signals of roller 10 are calculated using the extracted features by feature extractor 34. The power content is calculated each time a feature extraction occurs, which as described herein, may be eight times per second.

The power level, or power content of the responsive vibratory signals of roller 10 can be calculated as follows. Using i as the index in the frequency domain, such that i=1, . . . , n_(i), and ‘j’ as the index in the time domain such that j=1, . . . , n_(j), n_(i) represents the maximum number of features extracted from the vibration signal and n_(j) represents the maximum number of samples of the vibration signal. The spectrogram of the vibration signal can be represented by a matrix of n_(i) rows and n_(j) columns, where each element of the spectrogram ‘s’ represents the normalized power in a given feature at a particular instant in time (i.e., the square of the amplitude of the frequency). For example, the element in the i^(th) row and j^(th) column represents the normalized power contained in the i^(th) feature at the j*T_(s) instant in time, where T_(s) is the sample time.

If f_(i) is the frequency of the i^(th) feature, then the total power contained in the vibration signal at time index ‘j’ is calculated as,

${P_{j} = {\sum\limits_{i = 1}^{n^{i}}\left\lbrack {s_{ij}*\frac{\left( f_{i} \right)^{2}}{10^{6}}} \right\rbrack}},{j = 1},\ldots \mspace{14mu},{n_{j}.}$

For a set of ‘m’ consecutive time indices, the power feature of that set is calculated by

${P_{r} = {\frac{1}{m}{\sum\limits_{j = r}^{r + m - 1}P_{j}}}},$

r is the index of power feature of set of m consecutive time indices,

r=1, . . . , n_(r); n_(r)=n_(j)−m+1. An example showing the power contained in the vibration signal over successive roller passes over a stretch of pavement during its compaction is shown in FIG. 4. In the figure, the power index is set to three (3), that is the power content over three successive time instants is averaged to determine the average power content at a given instant. The three successive time instants may be, for example, three consecutive intervals of 0.125 seconds since as explained earlier, features may be extracted every 0.125 seconds.

Once the power content of the responsive vibratory signals of roller 10 are calculated, a spectrogram, like the one shown in FIG. 5, can be used to identify the locations on portion 40 where the maximum and minimum power occurred, and the locations of equally spaced power levels, for example, three equally spaced power levels therebetween. Generally, five identified power levels are designated as corresponding to minimum compaction level 0, equally spaced compaction levels 1, 2 and 3, and maximum compaction level 4.

The features extracted by feature extractor 34, namely the frequencies and the amplitudes of the frequencies are used as inputs to neural network 36. Neural network 36 will classify the features and identify the features as corresponding to one of the compaction levels 0, 1, 2, 3 or 4. As explained previously, each time a feature extraction occurs, 200 features representative of the responsive vibration signal of the roller at that time, namely, the 200 frequencies and the normalized power (squares of the amplitudes) of those frequencies are provided as inputs to the neural network. Only 200 features are utilized and those features in the lower range (i.e., 0-100 Hz) are ignored. The network will be trained so that the output of the neural network is one of compaction levels 0, 1, 2, 3, 4. The neural network will be trained to recognize the extracted features as being the same, or most similar to the features that correspond to one of the identified power levels, and will be classified accordingly. Thus, if the extracted features are most similar to the features that correspond to the minimum power level, the output of the neural network will be the indicator 0, for the minimum compaction level. If the extracted features are most similar to those contained in the maximum power signal, the output of the neural network will be the number 4, which indicates that the maximum compaction has been reached. The same process will occur when the extracted features are features that are most similar to those at one of the equally spaced power levels, in which case the output of the neural network will be one of the numbers 1, 2 or 3. During the training process, the interconnection weights of the neural network are modified to minimize the error between the output of the neural network and the level of compaction corresponding to each data set.

While density is a widely accepted method for acceptance testing finished pavement, density measurements are only an indirect measurement of the desired pavement property, which is stiffness. In addition to providing real time density readouts for a roadway during construction, the IACA 5 can likewise be utilized to provide real time indications of the stiffness of the road being constructed.

IACA 5 can be calibrated to estimate the dynamic modulus E, or M of the constructed road 40. The modulus M of each layer of the road 40 as it is constructed can be determined using the IACA, and thereafter the overall effective modulus E_(eff) of the road can be determined. The manner and method of calibration is like that disclosed with respect to density applied to dynamic modulus.

The initial calibration of IACA 5 thus assumes that compaction level 0 corresponds to the modulus of the asphalt mat at the lay-down density and the compaction level 4 corresponds to the target dynamic modulus M_(T) at the density specified in the mix design sheet (designed at 100 gyrations of the superpave gyratory compactor). After the IACA is trained to classify the vibrations into estimated levels of compactors, it is thus calibrated to reflect the modulus M of pavement layers, so that the overall E_(eff) for the constructed multi-layer pavement can be determined. To calibrate the IACA 5 for dynamic modulus, dynamic modulus tests are conducted in a lab for the mix used in the construction of each layer. M_(ld) is assumed to correspond to the dynamic modulus at the lay-down density of the layer, and thus corresponds to the lowest compaction level. The modulus value M_(T) at the target density of the compacted mix is assumed to be the highest modulus that can be achieved and corresponds to the highest compaction level. M_(ld) and M_(T) are determined by performing dynamic modulus tests for the asphalt mix being used in accordance with the AASHTO TP 62-03 test method. Master curves for the mix used are developed using the test to correlate the modulus with density. Curves are developed for the mix at different densities, for example 6%, 8%, 10% and 12% air voids. M_(ld) will be the modulus at 12% voids, and M_(T) will be the modulus at 6% voids—or 94% density. The construction of the master curves is explained in more detail below. The lay-down density of asphalt is generally assumed to be, for example, 85% to 88%, and the target or maximum density will generally be 94-97%. Compaction levels 1, 2 and 3 are designated as corresponding to equally spaced densities therebetween. Here, the curves are generated at 88%, 90%, 92% and 94% density.

The asphalt mixtures are thermorheologically simple materials and the time-temperature superposition principle is applicable in the linear viscoelastic state. Dynamic modulus and phase angle of asphalt mixtures can be shifted along the frequency axis to form single characteristic master curves at a desired reference temperature or frequency. The master curve for a mix is generated at a reference temperature of 21° C. using the procedure outlined in Practical Procedure for Developing Dynamic Modulus Master Curves to Pavement Structural Design. Transportation Research Record (2005) No. 1929, by R. Bonaquit and D. W. Christensen. (Practical Procedure) The following equations, which show the sigmoidal function and shift factor used for fitting the master curves, are used to develop the master curves as described in the Mechanistic-Empirical Pavement Design Guide and in accordance with AASHTO TP 62-03. A nonlinear optimization program, such as Solver in Microsoft Excel may be used for simultaneously solving these unknown parameters.

${\log {E^{*}}} = {\delta + \frac{\left( {{Max} - \delta} \right)}{1 + ^{\beta + {\gamma {\lbrack{{l\; {{og}{(f)}}} + {c{({10^{({A + {{VTS}\; {logT}_{R}}})} - {l\; {og}\; \eta_{t = r}}})}}}\rbrack}}}}}$

The shift factor used here was of the following form:

${a(T)} = \frac{f_{r}}{f}$

where, Max is the maximum |E*| for a particular mix, f_(r) is the reduced frequency at reference temperature, f is the frequency at a particular temperature, η_(t=r) is the viscosity of binder at reference temperature, A is the regression intercept of viscosity-temperature curve, VTS is the regression slope of viscosity-temperature susceptibility, a (T) is the shift factor as a function of temperature and age, and δ, β, γ, c are fitting parameters.

As with the density calibration, during the dynamic modulus calibration operation, roller 10 will make several passes on asphalt mat 18. Asphalt mat 18 may include portion 40 of the roadway section 42, which is a multi layer roadway, to be compacted. In the embodiment described, roadway section 42 is a three layer roadway section. The portion 40 will comprise a defined length, for example, thirty feet. Locations will be identified on the portion of the roadway, marked as locations A, B, C, D and E on FIG. 1. As shown in FIG. 6 the locations may be identified with a subscript to correspond to the individual layers. Locations for layer L1 may be identified as A₁, B₁, C₁, D₁, and E₁. Locations for layer L2 may be identified as A₂, B₂, C₂, D₂, and E₂. Locations for layer L1 may be identified as A₃, B₃, C₃, D₃, and E₃. The pattern will follow if more layers are used so that the locations will be A_(i)-E_(i), where i is the layer number. The locations A-E are exemplary and more or less locations my be used in the methods described herein. The modulus of each layer, L1, L2 and L3 will be used to obtain actual measured, or independently determined modulus of the layers of portion 40 of the roadway section 42. It is understood that roadway section 42 may extend for several miles and that once the calibration described herein has occurred, rolling of the remainder of the roadway section 42 can occur without further actual measurement of the modulus so long as the roadway section is comprised of the same roadway material as portion 42, based upon the output of the IACA 5 as indicated on an IACA display 44.

Prior to rolling portion 40, a plurality of initial inputs are entered into the compaction analyzer module 38. The initial inputs include the mix parameters of the roadway materials which may include, for example, type of construction (full depth, overlay, etc.), mix type, pavement lift, and lift thickness. Other initial inputs include the estimated target modulus M_(T) at the maximum density, and a minimum estimated modulus M_(ld) which may be the modulus at the lay-down density. M_(T) will be the target density as described herein. M_(T) and M_(ld) from the master curves will be at 21° C. The modulus value at other temperatures can be calculated by applying the correction factors developed in the master curves. Additional initial inputs to be entered into analyzer module 38 include an initial offset (off_(in)) which is an estimated, or assumed offset, or difference between the assumed modulus M_(ld) at the lay-down density and the actual modulus at the lay-down density, and an initial slope k_(in). The slope constant is simply the slope of a line running through M_(T) and M_(ld) and the compaction levels. In the described embodiment, k_(in) is (M_(T)−M_(id))/(n_(CL)−1), where n_(CL) is the number of compaction layers.

When roller 10 moves along layer L1 of portion 40 of roadway section 42, the GPS sensor 32 will trigger accelerometer 24 to begin collecting vibration data when location A is reached. The coordinates at the beginning A and end E of the portion 40 may be, for example, at the center of the width of the roadway portion 40. The coordinates will be utilized to start and stop the collection of responsive vibration signals of roller 10 as roller 10 passes over portion 40. The additional locations B, C and D may be, for example, at five, fifteen and twenty-five feet and are marked as well, at the center of the width of the portion 40 of the roadway section. When the features extracted by feature extractor 34 are classified by neural network 36, the compaction level will be an input to the analyzer module 38, which will utilize the initially entered input parameters and will generate a display of an estimated modulus in MegaPascals (MPa). The estimated modulus M_(est) will be calculated with the equation M_(est)=M_(ld)+k_(in)*C₁+off_(in) where C₁ is the level of compaction. off_(in) is assumed to be 0. For example, assuming a lay-down density l_(d) of 88% and a corresponding modulus M_(ld) of 2500 MPa, and a maximum estimated density of 96% and corresponding modulus M_(T) of 3500 MPa, with three equally spaced levels therebetween, an output of the neural network of 2 and the offset assumed to be 0, M_(est)=2500+(1000/4)(2)=3000 MPa. Analyzer module 38 will convert the compaction level into an estimated modulus in MPa.

It will be understood that because of the speed of the roller 10, and the rapidity of the pace at which samples are taken, the display, in the absence of any filtering, would likely rapidly alternate between estimated densities so that the display may be unreadable. Low pass filters can be used to smooth out the signal and provide a stable display without flicker to the user. Once no change in compaction in the layer being rolled is occurring, roller 10 ceases making passes, or moving along the portion 40. The modulus of layer L1 estimated by the IACA 5 after the initial calibration is based on the assumption that the target stiffness M_(T) for the specified mix for layer L1 is indeed achieved during compaction in the field. However, several features such as the compaction equipment, rolling pattern, lay-down temperature of the mix, lift thickness and other parameters may influence the actual modulus at any given location. In order to account for such deviations, an actual measured, or independently determined modulus is determined. One method for measuring is by using a Falling Weight Deflectometer (FWD) to determine the modulus. Measurements are taken using an FWD, for example, at locations A₁, B₁, C₁, D₁ and E₁ which were previously marked on the center of layer 1 portion 40 of roadway section 42. The measured modulus of each location is compared to the estimated modulus (i.e., M_(est)) at each of the identified locations. The locations and estimated level of compaction at each of the locations is determined through GPS measurements and the output of the neural network 36 as described. The location of the estimated modulus is available from the display, since the GPS unit 32 will provide the location at which the estimated modulus occur. The slope and offset are then adjusted, or modified to minimize the square of the error between the estimated and measured modulus. The adjusted or modified slope and offset are represented by k_(adj) and off_(adj).

Once both the measured and estimated moduli are known, the adjusted offset, is calculated as the mean error between the estimated and the measured densities so that

${off}_{adj} = {\frac{1}{n}{\sum\limits_{i = 1}^{n}\; {\left( {M_{meas}^{i} - M_{est}^{i}} \right).}}}$

where n is the number of locations at which a modulus is measured in this case at five locations. Thus, off_(adj) is the average error. The notations used in the derivation and steps used in calculating the adjusted slope and offset are as follows.

k—slope

off—offset

M_(ld)—modulus at lay-down density

C_(l) or _(lnn)—output of the neural network (compaction level)

M_(est)—estimated density of the neural network, and

M_(meas)—measured modulus.

The calibration scheme using the measured modulus is as follows. The new offset, off_(adj), is calculated as set forth above.

Assume n modulus measurements, M^(i) _(meas), i=1, . . . n, the corresponding estimated moduli are given by M^(l) _(est)=1, . . . , n, where M^(i) _(est)=M_(ld)+k_(in)*C_(l) ^(i)+off_(in), as described above.

The error between the raw estimates and the measured moduli are calculated as follows.

e_(i) = M_(est)^(i) − M_(meas)^(i) = M 1_(d) + k_(i n) × C_(l)^(i) + off_(i n) − M_(meas)^(i) $\begin{matrix} {{\sum\limits_{i = 1}^{n}\; e_{i}^{2}} = {\sum\limits_{i = 1}^{n}\left( {M_{ld} + {k \times C_{l}^{i}} + {off}_{i\; n} - M_{meas}^{i}} \right)^{2}}} \\ {= {\sum\limits_{i = 1}^{n}\left\lbrack {\left( {M_{ld} + {off}_{i\; n} - M_{meas}^{i}} \right) + {k*C_{l}^{i}}} \right\rbrack^{2}}} \\ {= {{\sum\limits_{i = 1}^{n}\left( {M_{ld} + {off}_{i\; n} - M_{meas}^{i}} \right)^{2}} + 2}} \\ {{{\sum\limits_{i = 1}^{n}\left\lbrack {\left( {M_{ld} + {off}_{i\; n} - M_{meas}^{i}} \right)*\left( {k*C_{l}^{i}} \right)} \right\rbrack} +}} \\ {{\sum\limits_{i = 1}^{n}\; \left( {k*C_{l}^{i}} \right)^{2}}} \end{matrix}$

Minimizing the mean square error (MSE), one obtains the desired adjusted stop slope k_(adj).

$\left. {\frac{}{k} = {{\sum\limits_{i = 1}^{n}\; e_{i}^{2}} = {\left. 0\Rightarrow{2{\sum\limits_{i = 1}^{n}\; {\left\lbrack {\left( {M_{ld} + {off}_{i\; n} - M_{meas}^{i}} \right)*C_{l}^{i}} \right\rbrack 2k{\sum\limits_{i = 1}^{n}\; \left( C_{l}^{i} \right)^{2}}}}} \right. = {\left. 0\Rightarrow{k{\sum\limits_{i\; 1}^{n}\; \left( C_{l}^{i} \right)^{2}}} \right. = {\sum\limits_{l = 1}^{n}\; \left\lbrack {\left( {M_{meas}^{i} - M_{ld} - {off}_{i\; n}} \right)*C_{l}^{i}} \right)}}}}} \right\rbrack$ $k_{adj} = \frac{\sum\limits_{i = 1}^{n}\left\lbrack {\left( {M_{meas}^{i} - M_{ld} - {off}_{{i\; n})}} \right){xC}_{l}^{i}} \right\rbrack}{\sum\limits_{i = 1}^{n}\left( C_{l}^{i} \right)^{2}}$

Once the adjusted offset and slope are determined, the initial input parameters are adjusted to utilize off_(adj) and k_(adj) in the density calculation in the analyzer module. Analyzer module 38 will use the equation M^(i) _(adj)=M_(ld)+k_(adj)*C_(l) ^(i)+off_(adj) to arrive at the adjusted modulus readout. The adjusted modulus M_(adj) is a more reliable indicator of actual stiffness of roadway portion 40 than is the estimated modulus. Once the selected initial input parameters have been adjusted, the roller 10 can roll the remainder of roadway section 42, and IACA display 44 will generate an adjusted density that can be viewed and relied upon by the operator. The roller 10 can make passes on roadway section 42 until the IACA display indicates a predetermined desired final stiffness, at which point roller 10 can be moved to another roadway section. If the additional roadway section has the same mix parameters as roadway section 42, there is no need for recalibration. The adjusted modulus is determined using the initial input parameters, except for the selected adjusted input parameters, namely, k_(adj) and off_(adj), along with the compaction level delivered to the analyzer module from the neural network.

The procedure described is used for each layer L(i) of the roadway being constructed. Once M_(adj) has been determined for each layer of the roadway, the effective modulus can be determined for the entire roadway. After the M_(adj) is determined for each layer, the overall modulus E_(eff) at any location on the roadway can be determined. Assuming a three-layer asphalt roadway 40 having layers L1, L2 and L3 the following equation yields E_(eff).

$E_{effective} = \left( \frac{{C_{2}\left( {{C_{1}h_{1}\sqrt[3]{{EL}_{1}}} + {h_{2}\sqrt[3]{{EL}_{2}}}} \right)} + {h_{3}\sqrt[3]{{EL}_{3}}}}{h_{1} + h_{2} + h_{3}} \right)^{3}$

EL₁, EL₂ and EL₃ are the dynamic modulus for layers L1, L2 and L3, respectively, and h₁, h₂ and h₃ are the thickness of the respective layers. C₁ and C₂ are correction factors utilized to obtain better agreement with the exact theory of elasticity as explained I P. Ullidtz, Modeling Flexible Pavement Response and Performance, Narayana Press, Odden, denmark, pp. 38-43 (1998). The value depends on layer thicknesses, modulus ratios, Poisson ratios and the number of layers. It is understood that the process can be extended using the Odemark method for transformation of a layered system.

In order to determine the initial M_(ld) and M_(T) to be used to determine M_(est), and to use as the initial inputs, master curves are developed based on the mix used in the construction of the road. The dynamic modulus master curves for the asphalt mix must be determined before the IACA calibration can occur. The master curves can be developed as described above by compacting the asphalt mix in a laboratory to obtain compacted specimens of 6%, 8%, 10% and 12% air voids. To obtain the desired results, a plurality of samples may be compacted for each target void. As described earlier, the mix may be preheated and compacted using a superpave gyratory compactor. Dynamic modulus tests may be conducted on the specimens using a MTS servo-hydraulic system in accordance with the test protocol set forth in AASHTO (2002) TP62-03. Testing is preferably performed at a plurality of temperatures, for example, 4° C., 21° C., 40° C. and 55° C. For each temperature level, tests may be conducted at a plurality of frequencies. As described above, master curves are generated for the different air void levels (6%, 8%, 10% and 12%) at a reference temperature of 21° C. using the procedure outlined in Practical Procedure

Once the master curves are developed, modulus for the curves at 12% density and 6% density is used to calibrate the IACA.

While EL₁, EL₂ and EL₃ are preferably determined using an FWD, there are occasions in which testing can not be conducted. There are at least two other methods that can be used to ,determine EL₁, EL₂ and EL₃. If it is not possible to conduct FWD tests, cores can be cut at locations A_(i)-E and the densities of the cores determined using known methods. The master curves can then be utilized to find the corresponding modulus, which will be used as the M_(meas) in the calculations expressed herein. If it is not possible to construct Dynamic Modulus Master Curves for estimating modulus from density, there are known empirical models developed for known mixes, which can be used to supply M_(meas).

The following is an example of the use of the method for determining stiffness.

The use of the IACA in estimating the stiffness of a multi layer HMA pavement was investigated during the construction of Interstate I-35 in Norman, Okla. This project involved the expansion of the existing highway, stabilizing the subgrade to a depth of 200 mm using 10% cement kiln dust (CKD), followed by 200 mm thick aggregate base. The base layer was consisted of 100 mm thick asphalt layers of 19 mm Nominal Maximum Aggregate Size (NMAS) S3 (64-22 OK), while 2^(nd) and 3^(rd) layer were constructed with 19 mm NMAS S3 (76-28 OK) consisted of 100 mm and 75 mm thickness, respectively.

Material and Sample Preparation. The loose HMA mixes of type S3 (PG 64-22 OK) and S3 (PG76-28) were collected from the construction site during the time of pavement construction. The S3 (PG 64-22) type of mix was used in base layer, while, S3 (PG 76-28) mix was used in 2^(nd) and 3^(rd) layers of pavement. The nominal maximum aggregate (primarily limestone) size for all mixes was 19 mm. The base mix contained approximately 20 percent 1″ rock, 44 percent manufactured sand, 11 percent sand, and 25 percent recycled asphalt pavement (RAP), and 4.1 percent PG 64-22 OK binder. The 2^(nd) and 3^(rd) layer mixes contained approximately 22 percent 1″ rock, 50 percent manufactured sand, 13 percent sand, and 15 percent recycled asphalt pavement (RAP), and 4.1 percent PG 76-28 OK binder. The gradations and other volumetric properties of all HMA mixes are given in Table 1 and Table 2. The loose HMA mixes were preheated in an oven, and samples were compacted using a Superpave Gyratory Compactor (SGC). Three replicates of samples were compacted at 6, 8, 10, and 12%±1% target air voids levels. Initially, samples having 150 mm in diameter×167.5 mm in height were prepared. Then, the test specimens of 100 mm in diameter were cored from the center of the gyratory compacted specimens, and sawed from each end of the specimen to get final sample of size 100 mm in diameter×150 mm in height. The volumetric analysis was conducted to obtain effective binder content (V_(beff)), the voids in mineral aggregates (VMA), the voids filled with asphalt (VFA), and the air voids (V_(a)) for all the mixes (Table 3).

TABLE 1 Gradation of All HMA Mixes Material (%) Base Layer 2^(nd) and 3^(rd) Layer 1″ Rock 20 22 Manufactured Sand 44 50 Sand 11 13 RAP 25 15 Sieve Size Gradation (% Passing) 25 100 100 19 98 98 12.5 87 87 9.5 80 80 4.75 58 62 2.36 37 40 1.18 25 27 0.6 19 20 0.3 12 12 0.15 4 5 0.075 2.9 2.8 RAP = Reclaimed Asphalt Pavement

TABLE 2 Materials Volumetric Properties Volumetric Properties Base Layer 2^(nd) and 3^(rd) Layer G_(mm)  2.505  2.523 G

 2.671  2.677 G

 2.645  2.657 G_(b) 1.01 1.01 Binder Type PG 64-22 PG 76-28 P_(b) (%) 4.1  4.1  VMA (%) Min. 14.1  14.81  Max. 20.4  20    VFA (%) Min. 39.9  41.9  Max. 62.2  60.8  Va (%) 6, 8, 10, 12 Aggregate Type Limestone Limestone Mix Type Recycled Recycled G_(mm) = Maximum Theoretical Specific Gravity Mixture G

 = Bulk Specific Gravity of Aggregate G

 = Effective Specific Gravity of Aggregate G_(b) = Specific Gravity of Binder P_(b) = Asphalt Content VMA = Voids in Mineral Aggregates VFA = Voids Filled with Asphalt V

 = Air Voids

indicates data missing or illegible when filed

TABLE 3 Specimens Volumetric Properties for all HMA Mixes Base Layer (Mix-S3 64-22) 2^(nd) and 3^(rd) Layer (Mix S3 76-28) Target Air Sample Sample Voids (%) (%) 1 2 3 1 2 3 6 V_(u) 5.4 5.6 5.6 6.5 6.4 6.4 VMA 14.1 14.3 14.3 14.9 14.8 14.7 VFA 62.2 61.4 61.5 60.1 60.4 60.8 V_(beff) 8.8 8.8 8.8 8.9 8.9 9.0 8 V_(a) 7.3 7.2 7.2 8.3 8.1 7.9 VMA 15.8 15.7 15.7 16.5 16.3 16.1 VFA 54.5 54.7 54.9 53.3 53.9 54.6 V_(beff) 8.6 8.6 8.6 8.8 8.8 8.8 10 V_(a) 9.3 9.6 9.1 9.6 10.2 9.8 VMA 17.7 17.9 17.5 17.7 18.3 17.9 VFA 47.7 46.9 48.3 48.9 47.0 48.3 V_(beff) 8.4 8.4 8.4 8.6 8.6 8.6 12 V_(a) 11.5 12.4 12.4 12.2 11.7 12.0 VMA 19.7 20.4 20.4 20.0 19.6 19.9 VFA 41.8 39.9 39.9 41.9 43.2 42.3 V_(beff) 8.2 8.1 8.1 8.4 8.4 8.4 V_(a) = Air Voids VMA = Voids in Mineral Aggregates VFA = Voids Filled with Asphalt V_(beff) = Effective asphalt content by volume

Dynamic Modulus Testing

Dynamic modulus was measured for all collected mixes at four different air voids: 6%, 8%, 10%, and 12%. All dynamic modulus tests were performed using a MTS servo-hydraulic testing system. The test specimen was placed in an environmental chamber and allowed to equilibrium to the specified testing temperature +0.5° C. The specimen temperature was monitored using a dummy specimen with a thermocouple mounted at the center. Two linear variable differential transducer (LVDTs) were mounted on the specimen. Friction reducing end treatment, two teflon papers were placed between the specimen ands and loading plates. To begin testing, a minimal contact load was applied to the specimen. A sinusoidal axial compressive load was applied to the specimen without impact in a cyclic manner. The test was run on each test specimen at four different temperatures, including 4, 21, 40, and 55° C., and the test started from the lowest temperature to the highest temperature. For each temperature level, the test was run at different frequencies from the highest to the lowest, including 25 , 10, 5, 1, 0.5, 0.1 Hz. Prior to testing, the sample was conditioned by applying 200 cycles of load at a frequency of 25 Hz. The load magnitude was adjusted based on the material stiffness, air void content, temperature, and frequency to keep the strain response within 50-150 micro-strains. The data was recorded for the last 5 cycles of each sequence. The dynamic modulus tests were performed according to the AASHTO TP62-03.

Construction of the Master Curves

The master curves are generated at a reference temperature of 21° C. using the procedure outlined above, and the equations set forth above and reproduced below:

$\begin{matrix} {{\log {E^{*}}} = {\delta + {\frac{\left( {{Max} - \delta} \right)}{1 + ^{\beta + {\gamma {\lbrack{{l\; {{og}{(f)}}} + {c{({10^{({A + {{VTS}\; {logT}_{R}}})} - {l\; {og}\; \eta_{t = r}}})}}}\rbrack}}}}\text{:}}}} & (5) \\ {{a(T)} = \frac{f_{r}}{f}} & (6) \end{matrix}$

1000691 The A and VTS parameters for PG 64-22 (10.98, −3,680), and PG 76-28 (9.2, −3.024) were taken from the MEPDG guide. The constructed master curves for base, 2nd and 3^(rd) layers are shown in FIG. 3 and FIG. 4. It can be seen from FIG. 3, and FIG. 4 that dynamic modulus value decreases as air voids increases. The developed master curves were used to estimate dynamic modulus of each layers at any air voids levels, and temperature. The ‘goodness-of-fit’ statistic, S_(e)/S_(y) (standard error of the estimated/standard deviation), and correlation coefficient, (R²), were used to assess the validity of the correlation between laboratory measured and master curve fit equation. Based on these criteria, the developed master curve equations in this study were found to be in excellent correlation with laboratory measured data. The coefficients and the fitting statistics of the master curves are summarized in Table 4.

TABLE 4 Master Curves Parameters Air Voids (%) Max E* (MPa) δ β γ c R² S_(e)/S_(γ) Fit Base Layer (Mix-S3 64-22) 6 23084 1.81 −1.02 −0.43 1.20 0.99 0.07 Excellent 8 22256 1.54 −0.98 −0.39 1.20 0.99 0.05 Excellent 10 21232 1.23 −0.86 −0.37 1.04 0.99 0.06 Excellent 12 19942 1.72 −0.41 −0.40 1.05 0.99 0.08 Excellent 2^(nd) and 3^(rd) Layer (Mix-S3 76-28) 6 22826 2.10 −0.25 −0.45 1.24 0.99 0.04 Excellent 8 22027 1.99 −0.24 −0.42 1.18 0.99 0.05 Excellent 10 21157 1.98 −0.17 −0.42 1.12 0.99 0.04 Excellent 12 20182 1.71 −0.12 −0.37 1.13 0.99 0.05 Excellent Shift Factors log(aT) Base Layer (Mix-S3 64-22) 2nd and 3rd Layer (Mix-S3 76-28) Air Voids (%) 4° C. 21° C. 40° C. 55° C. 4° C. 21° C. 40° C. 55° C. 6 2.66 0.00 −2.23 −3.60 2.24 0.00 −1.96 −3.20 8 2.65 0.00 −2.22 −3.58 2.13 0.00 −1.86 −3.04 10 2.30 0.00 −1.93 −3.11 2.02 0.00 −1.77 −2.89 12 2.32 0.00 −1.95 −3.14 2.04 0.00 −1.78 −2.91

Measurement of Density using IACA

The use of the IACA in estimating the stiffness of a multi layer HMA pavement Was investigated during the construction of Interstate I-35 in Norman, Okla. A test section of 450 feet was selected and seven test locations, approximately 20 meters apart, were marked on the center line of the lane for verification analysis. The test procedure and results are now discussed.

The IACA data was collected during the compaction of the all three layers (base, 2^(nd) layer, and 3^(rd) layer). First, the test points were marked on base layer, and the IACA data was collected. The GPS location of these points was recorded to locate these test locations on each pavement layer. Similar points were marked on 2^(nd) and 3^(rd) layers and the IACA data was collected during the compaction of each of these layers. The IACA data was analyzed to get the density estimate of each layers. It is known that the IACA measurements are typically within 1% of the density measured from pavement cores (10-11). The measured density of each layer is given in Table 5. The density for base layer varies from 89.4% to 93.3%, similiarly the density of 2^(nd) and 3^(rd) layers vary from 89.5% to 88.9%, and 9L8 5% to 93.3%, respectively. It can be seen that the density at each location changes with the layer types, with most consistent density was observed on top layer. Such variation in the density in three layer might affect stiffness of combined layer. These density were converted into the air voids (% air voids=100-% density) to estimate dynamic modulus of of each location.

TABLE 5 IACA Measured Density of Each Layer Test IACA Estimated Density (%) Point Base Layer 2^(nd) Layer 3^(rd) Layer T8 92.5 88.9 91.8 T1N 91.9 90.6 92.9 T2N 91.6 92.3 93.2 T3N 93.3 90.9 92.3 T4N 91.7 92.1 92.1 T5N 90.9 92.3 92.2 M6 89.4 89.5 93.3

Estimating the Effective Modulus of Pavement Layers

The FWD measured modulus is compared with the actual effective modulus of the layers using the Odemark method of equivalent thickness. Odemark method is used to transform a system consisting of layers with different moduli into an equivalent system where the thicknesses of the layers are altered but all layers have the same modulus. The transformation assumes that the stiffness of the layer remains the same, i.e. I×E/(1−μ²) remains constant where I=moment of inertia; E=layer modulus; and μ□=Poisson ratio (19-22).

This approach is used in the present paper to calculate the effective modulus of the three layers that constitute the pavement on I-35. The IACA data collected during the compaction of each of the pavement layers is first used to determine the dynamic modulus at each of the each test locations. The effective modulus (E_(effective) or E_(eff)) of three layers of pavement was calculated using Equation 7. The effective moduli were calculated at 21° C. and 5 Hz frequency (Table 6).The similar approach was used by several other researchers to find the effective modulus for layered system of pavement (23-25).

$E_{effective} = \left( \frac{{C_{2}\left( {{C_{1}h_{1}\sqrt[3]{{EL}_{1}}} + {h_{2}\sqrt[3]{{EL}_{2}}}} \right)} + {h_{3}\sqrt[3]{{EL}_{3}}}}{h_{1} + h_{2} + h_{3}} \right)^{3}$

E₁, E₂ and E₃ are dynamic modulus of top, 2^(nd), and base layer, and h₁, h₂, and h₃ are the thickness of respective layers. C₁, and C₂ are the correction factors to obtain better agreement with exact theory of elasticity, (21, 26). The value of correction factors depend on the layer thicknesses, modular ratios, Poisson ratios and the number of layers in pavement structure. In the present study correction factors were taken as C₁=1 while C₂=0.8.

TABLE 6 Effective Modulus and FWD Modulus of Three Layers of Pavement Measured Dynamic Modulus (MPa) Effective FWD Point Base Layer 2^(nd) Layer 3^(rd) Layer Modulus (MPa) Modulus (MPa) T8 5406 2190 3049 2365 3062 T1N 5070 2659 3456 2502 2482 T2N 4910 3227 3576 2637 2353 T3N 5889 2751 3227 2667 2696 T4N 4963 3155 3155 2554 2878 T5N 4556 3227 3191 2482 2657 M6 3880 2345 3617 2161 2760

Verification of the IACA measured Pavement Modulus. The verification of the IACA measured modulus was done by conducting FWD testing on seven test locations that were marked before for estimating density using the IACA. The FWD is a non-destructive test device used to characterize the in-situ pavement moduli (15, 27). It drops a transient load from a specified height on a 300 mm diameter circular plate with a thin rubber pad mounted underneath. The load and deflection is measured using load cell and sensors set on the ground. Seven sensors were placed at 0, 200, 300, 450, 600, 900, and 1500 mm away from the center of the loading plate. In the present study the FWD test was conducted on 3^(rd) layer of pavement using a Dynatest FWD test system. Numerical back-calculation software, MODULUS 6.0, was used to process the FWD raw data so as to determine the modulus value (28). The back-calculated modulus is often called the effective modulus because the value represents the effect of the layer within the whole pavement structure. The effective modulus was calculated at 21° C. to compare this modulus with laboratory measured effective dynamic modulus. Since, the FWD loading induces a pulse of duration of 0.03 s (29), which is equivalent to a test frequency of 5.3 Hz (1/0.03/2π), hence, the comparisons in this paper are performed using modulus values calculated at 21° C. and 5 Hz frequency. Table 6 shows the results of the FWD test. FIG. 3. below shows that the modulus estimated by the proposed method is in good agreement with the FWD measurements.

Thus, it is seen that the apparatus and methods of the present invention readily achieve the ends and advantages mentioned as well as those inherent therein. While certain preferred embodiments of the invention have been illustrated and described for purposes of the present disclosure, numerous changes in the arrangement and construction of parts and steps may be made by those skilled in the art, which changes are encompassed within the scope and spirit of the present invention as defined by the appended claims. 

1. A method of compacting a multi-layer roadway section with a roller having a compaction analyzer operably associated therewith comprising: entering initial input parameters of the first layer of the roadway section into the compaction analyzer; making a plurality of passes with the roller over the first layer of a portion of the roadway section; applying a vibratory energy to the first layer of the portion of the roadway section with the roller as it moves thereover; repeatedly gathering responsive vibration signals of the roller as it moves over the first layer portion of the roadway section; generating, with the compaction analyzer, estimated dynamic modulus signals representative of estimated moduli based upon the responsive vibration signals of the roller and the initial input parameters entered into the compaction analyzer; measuring the dynamic modulus of the first layer of the roadway section at a plurality of locations on the portion of the roadway section; comparing the measured modulus with the estimated modulus at the plurality of locations to determine the difference between the measured and the estimated moduli; adjusting selected ones of the initial input parameters to the analyzer based on the difference between the determined modulus and the estimated modulus so that an adjusted modulus output signal generated by the compaction analyzer will more closely approximate an actual modulus of the roadway section than does the estimated modulus signal; and rolling the remainder of the roadway section until the compaction analyzer with the adjusted input parameters generates a desired adjusted output modulus signal.
 2. The method of claim 1, wherein the initial input parameters include mix characteristics of roadway material, an estimated minimum modulus (M_(ld)) and an estimated maximum modulus (M_(T)) for the first layer.
 3. The method of claim 1, wherein (M_(ld)) is the modulus at a specified lay-down density and M_(T) is the modulus a target density achieved in a mix specification for the roadway material used in the first layer.
 4. The method of claim 3, further comprising: identifying the responsive vibration signals with the highest power, the lowest power, and equally spaced power levels therebetween; and designating specified minimum, maximum and equally spaced compaction levels as corresponding to the responsive vibration signals with the highest, lowest, and equally spaced powers; delivering the compaction levels to an analyzer module of the compaction analyzer; and generating the estimated modulus (M_(est)) of the first layer portion of the roadway section in real time with the formula M_(est)=M_(ld)+k_(in)*(C_(l))+off_(in), where k_(in) is an initial slope parameter that is an initial input parameter, off_(in) is an estimated offset from the minimum estimated modulus and is also an initial offset parameter, and C_(l) is the compaction level delivered to the analyzer module.
 5. The method of claim 4, wherein the adjusting step comprises adjusting the initial slope and offset parameters, so that the compaction analyzer will generate an adjusted density (M_(adj)) with the formula M_(adj)=M_(ld)+k_(adj)(C_(l))+offset_(adj), where k_(adj) and off_(adj) are the adjusted slope and offset parameters respectively.
 6. The method of claim 4 wherein the power of a given responsive vibration signal is calculated using the equation $p = {\sum\limits_{i = 1}^{n}\; \left\lbrack {S_{i}*\frac{\left( f_{i} \right)^{2}}{10^{6}}} \right\rbrack}$ where f_(i) represents a plurality of frequencies contained in the given responsive vibration signal and S_(i) is the square of the amplitude of the frequencies.
 7. The method of claim 6 wherein the initial slope parameter k_(in) is represented by the equation k_(in)=M_(T)−M_(ld)/n_(cl)−1 where n_(cl) is the total number of compaction levels, and wherein the estimated initial offset is zero.
 8. The method of claim 7, wherein the adjusting step comprises adjusting the initial slope and offset parameters, and generating an adjusted density (M_(adj)) with the formula M_(adj)=M+k_(adj)(C_(l))+offset_(adj), where k_(adj) and off_(adj) are the adjusted slope and offset parameters respectively.
 9. The method of claim 8, wherein the adjusted offset is calculated using the equation ${off}_{adj} = {\frac{1}{n}{\sum\limits_{i = 1}^{n}\; \left( {M_{meas}^{i} - M_{est}^{i}} \right)}}$ where n is the number of the plurality of locations at which density is measured, M_(est) is the estimated modulus at the plurality of locations, M_(meas) is the measured modulus at the plurality of locations and the adjusted slope is calculated using the equation $k_{adj} = {\sum\limits_{i = 1}^{n}\; \frac{\left. {\left\lbrack {M_{meas}^{i} - M_{ld} - {off}_{adj}} \right)x\; C_{l}^{i}} \right\rbrack}{\sum\limits_{i = 1}^{n}\; \left( C_{l}^{i} \right)^{2}}}$
 10. A method of compacting, comprising performing the steps of claims 1 through 5 on each additional layer of the portion of the roadway section to determine M_(adj) for each layer of the roadway section.
 11. The method of claim 10 further comprising determining an overall effective modulus E_(eff) based on the M_(adj) for each layer of the roadway section.
 12. The method of claim 11, where the roadway is a three layer roadway section, and E_(eff) is determined using the equation $E_{effective} = \left( \frac{{C_{2}\left( {{C_{1}h_{1}\sqrt[3]{{EL}_{1}}} + {h_{2}\sqrt[3]{{EL}_{2}}}} \right)} + {h_{3}\sqrt[3]{{EL}_{3}}}}{h_{1} + h_{2} + h_{3}} \right)^{3}$ where EL₁, EL₂ and EL₃ are the dynamic modulus for layers L1, L2 and L3, respectively, and h₁, h₂ and h₃ are the thickness of the respective layers and are correction factors.
 13. A method of determining the stiffness of a multi layer roadway comprising: (a) making a plurality of passes with a roller over the first layer of the roadway section; (b) applying a vibratory energy to the first layer of the portion of the roadway section with the roller; (c) generating, with a compaction analyzer operably associated with the roller, estimated modulus signals based upon the responsive vibration signals of the roller; (d) independently determining the dynamic modulus at a plurality of locations on the first layer; (e) adjusting selected ones of input parameters for the compaction analyzer based on the differences between the estimated modulus and the independently determined modulus at the plurality of locations to arrive at an adjusted modulus that more closely approximates the actual modulus than the estimated modulus; (f) performing steps (a)-(e) for each layer of the roadway section; and (g) calculating an overall modulus E_(eff) using the adjusted modulus M_(adj) for each layer of the roadway.
 14. The method of claim 13 wherein the independently determining step comprises: determining the modulus at the plurality of locations with a falling weight deflectometer.
 15. The method of claim 14 wherein the roadway is a three layer roadway, and E_(eff) is calculated with the following equation $E_{effective} = \left( \frac{{C_{2}\left( {{C_{1}h_{1}\sqrt[3]{{EL}_{1}}} + {h_{2}\sqrt[3]{{EL}_{2}}}} \right)} + {h_{3}\sqrt[3]{{EL}_{3}}}}{h_{1} + h_{2} + h_{3}} \right)^{3}$ where EL₁, EL₂ and EL₃ are the dynamic modulus for layers L1, L2 and L3, respectively, and h₁, h₂ and h₃ are the thickness of the respective layers and C₁ and C₂ are correction factors.
 16. The method of claim 15, wherein the initial input parameters include mix characteristics of roadway material, an estimated minimum modulus (M_(ld)) and an estimated maximum modulus (M_(T)) for the first layer.
 17. The method of claim 16, wherein (M_(ld)) is the modulus specified lay-down density and M_(T) is the modulus a target density achieved in a mix specification for the roadway material.
 18. The method of claim 17, further comprising: identifying the responsive vibration signals with the highest power, the lowest power, and equally spaced power levels therebetween; and designating specified minimum, maximum and equally spaced compaction levels as corresponding to the responsive vibration signals with the highest, lowest, and equally spaced powers; delivering the compaction levels to an analyzer module of the compaction analyzer; and generating the estimated modulus (M_(est)) of the first layer portion of the roadway section in real time with the formula M_(est)=M_(ld)+k_(in)*(C_(l))+off_(in), where k_(in) is an initial slope parameter that is an initial input parameter, off_(in) is an estimated offset from the minimum estimated modulus and is also an initial offset parameter, and C_(l) is the compaction level delivered to the analyzer module.
 19. The method of claim 18, wherein the adjusting step comprises adjusting the initial slope and offset parameters, so that the compaction analyzer will generate an adjusted density (M_(adj)) with the formula M_(adj)=M_(ld)+k_(adj)*(C_(l))+offset_(adj), where k_(adj) and off_(adj) are the adjusted slope and offset parameters respectively.
 20. The method of claim 13, wherein the independently determining step comprises: cutting cores from the plurality of locations, measuring the density of the cores; and finding the modulus that corresponds to the measured density based on master curves for the mix used for each layer respectively.
 21. The method of claim 13, wherein the independently determining step comprises using known empirical models for the mixes to determine the modulus.
 22. A method of determining the stiffness of a roadway comprising: compacting the asphalt mix to be used for each layer of the roadway to obtain a plurality of laboratory specimens of a plurality of densities for each layer; determining a laydown modulus M_(ld) and a target modulus M_(T) that correspond to the laydown and target densities of the specimens for each layer; using the laydown modulus and the target modulus of each layer to calculate a modulus of each roadway layer; and calculating an overall effective modulus for the roadway using the modulus of each layer.
 23. The method of claim 22 wherein the using step comprises: making a plurality of passes with a roller having a compaction analyzer operably associate therewith over each layer of a portion of the roadway section beginning with the first layer; applying a vibratory energy to each layer of the portion of the roadway section with the roller as it moves thereover; repeatedly gathering responsive vibration signals of the roller as it moves over each layer portion of the roadway section; calculating an estimated modulus M_(est) of each layer of the roadway section with the formula M_(est)=M_(ld)+k_(in) (C₁)+off_(in) at a plurality of locations on each layer, where an initial slope parameter k_(in) is (M_(T)−M_(ld))/(n_(CL)−1) and an initial input parameter, off_(in) is an estimated offset from the minimum estimated modulus and is also an initial offset parameter, C_(l) is the compaction level delivered to the analyzer module and n_(CL) is the number of compaction levels; measuring the dynamic modulus of each layer of the roadway section at the plurality of locations on the portion of the roadway section; comparing the measured modulus with the estimated modulus at the plurality of locations to determine the difference between the measured and the estimated moduli; and adjusting selected ones of the initial input parameters to the analyzer based on the difference between the determined modulus and the estimated modulus so that an adjusted modulus output signal generated by the compaction analyzer will more closely approximate an actual modulus of the roadway section than does the estimated modulus signal, the adjusting step comprising adjusting the initial slope and offset parameters, so that the compaction analyzer will generate an adjusted density (M_(adj)) with the formula M_(adj)=M_(ld)+k_(adj)(C_(l))+offset_(adj), where k_(adj) and off_(adj) are the adjusted slope and offset parameters respectively.
 24. The method of claim 23, wherein the road is a three-layer road, and wherein the overall modulus for the road is calculated using the equation: $E_{effective} = \left( \frac{{C_{2}\left( {{C_{1}h_{1}\sqrt[3]{{EL}_{1}}} + {h_{2}\sqrt[3]{{EL}_{2}}}} \right)} + {h_{3}\sqrt[3]{{EL}_{3}}}}{h_{1} + h_{2} + h_{3}} \right)^{3}$ where EL₁, EL₂ and EL₃ are the dynamic modulus for layers L1, L2 and L3, respectively, and h₁, h₂ and h₃ are the thickness of the respective layers and C₁ and C₂ are correction factors.
 25. The method of claim 23, the determining step comprising: creating master curves to represent the relationship between the density of the specimens and the modulus of the specimens for each layer; and locating M_(ld) and the M_(T) on the master curves.
 26. The method of claim 23, wherein the measuring step comprises using an FWD to find the modulus at the plurality of locations.
 27. A method of compacting a multi-layer road comprising: determining a modulus at a plurality of locations on each layer; and calculating an overall effective modulus for the roadway using the modulus for each of the layers.
 28. The method of claim 27, wherein the roadway is a three-layer roadway and the modulus is calculated using the equation: $E_{effective} = \left( \frac{{C_{2}\left( {{C_{1}h_{1}\sqrt[3]{{EL}_{1}}} + {h_{2}\sqrt[3]{{EL}_{2}}}} \right)} + {h_{3}\sqrt[3]{{EL}_{3}}}}{h_{1} + h_{2} + h_{3}} \right)^{3}$ where EL₁, EL₂ and EL₃ are the dynamic modulus for layers L1, L2 and L3, respectively, and h₁, h₂ and h₃ are the thickness of the respective layers and C₁ and C₂ are correction factors.
 29. The method of claim 26, the determining step comprising: making a plurality of passes with a roller having a compaction analyzer over each layer of a portion of the roadway section; applying a vibratory energy to each layer of the portion of the roadway section with the roller as it moves thereover; repeatedly gathering responsive vibration signals of the roller as it moves over the first layer portion of the roadway section; generating, with the compaction analyzer, estimated dynamic modulus signals representative of estimated moduli based upon the responsive vibration signals of the roller and the initial input parameters entered into the compaction analyzer; measuring the dynamic modulus of the first layer of the roadway section at a plurality of locations on the portion of the roadway section; comparing the measured modulus with the estimated modulus at the plurality of locations to determine the difference between the measured and the estimated moduli; adjusting selected ones of the initial input parameters to the analyzer based on the difference between the determined modulus and the estimated modulus so that an adjusted modulus output signal generated by the compaction analyzer will more closely approximate an actual modulus of the roadway section than does the estimated modulus signal.
 30. The method of claim 27, further comprising rolling the remainder of each layer of the roadway section until the compaction analyzer with the adjusted input parameters generates a desired adjusted output modulus signal. 